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X-Rays from Accelerated Ion Interactions
Vincent Tatischeff
Laboratory for High Energy Astrophysics
Goddard Space Flight Center, Greenbelt, MD 20771
Reuven Ramaty
Laboratory for High Energy Astrophysics
Goddard Space Flight Center, Greenbelt, MD 20771
and
Benzion Kozlovsky
Sackler Faculty of Exact Science, Tel Aviv University
Ramat Aviv, Tel Aviv, Israel
ABSTRACT
We have developed in detail the theory of X-ray line and continuum production due
to atomic interactions of accelerated ions, incorporating in our calculations information
from a broad range of laboratory measurements. We applied our calculations to the
Orion region from which nuclear gamma-ray lines were observed with the COMPTEL
instrument on CGRO. The accelerated particles which produce this gamma-ray
emission via nuclear reactions also produce X-ray lines via atomic interactions. We
predict strong line emission in the range from 0.5 to 1 keV, mainly due to de-excitations
in fast O ions. While much of the diffuse X-ray emission observed with ROSAT
from Orion could be due to accelerated ions, the current X-ray data do not provide
unambiguous signatures for such an origin. If future observations with high spectral
resolution would confirm the predicted X-rays, the combined analysis of the X-ray
and gamma-ray data will set important constraints on the origin of the accelerated
particles and their interaction model.
Subject headings: acceleration of particles–atomic processes–line:formation –ISM:
individual (Orion)–gamma rays: theory–X-rays: general
– 2 –
1. Introduction
Strong gamma-ray emission in the 3-7 MeV range has been detected from the Orion molecular
cloud complex with the COMPTEL instrument on the Compton Gamma Ray Observatory
(CGRO; Bloemen et al. 1994, 1997). As the observed spectrum exhibits characteristic structures
(Bloemen et al. 1997), this emission is most likely due to the superposition of nuclear gamma-ray
lines, mainly the 4.44 MeV line from 12C and the 6.13, 6.92 and 7.12 MeV lines from 16O. Such
line emission can only be produced by accelerated particle interactions. Gamma-ray emission
at photon energies >30 MeV was also observed from Orion, with the EGRET instrument on
CGRO (Digel, Hunter, & Mukherjee 1995). This gamma-ray emission is consistent with pion
production and bremsstrahlung due to irradiation by standard Galactic cosmic rays (Digel et al.
1995). As such cosmic rays underproduce the observed line emission by at least three orders of
magnitude, the gamma-ray line production in Orion must predominantly be a low energy cosmic
ray phenomenon. Information on the spatial distribution of the gamma-ray line emission in Orion
has come from both the COMPTEL and CGRO/OSSE observations. The extended nature of the
emission seen in the COMPTEL map of Orion (Bloemen et al. 1997) could provide an explanation
for the fact that so far it was not possible to confirm the COMPTEL results with OSSE (Murphy
et al. 1996; Harris et al. 1998).
Based on the observed line widths, Bloemen et al. (1994) first suggested that the line emission
is produced by accelerated C and O ions interacting with ambient H and He, rather than by
accelerated protons and α-particles interacting with ambient C and O. More detailed analyses
of the initial COMPTEL data have shown that a mix of the two processes could not be ruled
out (Ramaty, Kozlovsky, & Lingenfelter 1995; Cowsik & Friedlander 1995). But, as the emission
peaks in the more recent COMPTEL data do not appear at the line center energies for 12C and16O de-excitations (Bloemen et al. 1997), a significant narrow-line contribution from accelerated
proton and α-particle interactions seems to be excluded (Kozlovsky, Ramaty, & Lingenfelter 1997).
This conclusion is also supported by energetic arguments, as the very large power deposited by the
accelerated particles into the ambient medium in Orion is lowered by enhancing the C-to-proton
and O-to proton abundance ratios (Ramaty et al. 1995; Ramaty, Kozlovsky & Lingenfelter 1996).
Apart from the observed emission in the 3-7 MeV band, the COMPTEL observations revealed
only upper limits at other gamma-ray energies (Bloemen et al. 1994, 1997). In particular, the
upper limit on the 1-3 MeV emission sets constraints on the accelerated Ne-Fe abundances relative
to those of C and O. The suppression of both the Ne-Fe and proton and α-particle abundances
relative to C and O could be understood if the seed particles injected into an as-yet unknown
particle accelerator (see Nath & Biermann 1994; Bykov & Bloemen 1994) come from the winds of
massive stars or the ejecta of supernovae resulting from massive progenitors (Bykov & Bloemen
1994; Ramaty et al. 1995; Casse, Lehoucq, & Vangioni-Flam 1995; Ramaty et al. 1996; Parizot,
Casse, & Vangioni-Flam 1997a). Ip (1995) and Ramaty et al. (1996) have also considered the
possible acceleration of ions resulting from the breakup of interstellar dust.
The gamma-ray line production in Orion should be accompanied by a large ionization rate of
– 3 –
the ambient medium which could exceed the observed infrared luminosity (Cowsik & Friedlander
1995). This problem is alleviated if the gamma-rays are produced at cloud boundaries, but not
in their interiors. The accelerated particles could have ionized ∼2×104M⊙ in 105 years (Ramaty
1996), a small fraction of the total available mass. It is thus possible that a large fraction of the
power that accompanies the gamma-ray production is deposited in an ionized gas.
While the X-ray emission produced by low energy particle interactions is potentially a
promising tracer of low energy cosmic rays in the Galaxy (e.g. Hayakawa & Matsuoka 1964),
there are as-yet no astrophysical X-ray observations that unambiguously indicate the presence
of such cosmic rays. The Orion region, however, has become an interesting target owing to the
COMPTEL discovery of the nuclear gamma-ray line emission. A variety of processes lead to X-ray
production by low energy ion interactions. Inverse bremsstrahlung (Boldt & Serlemitsos 1969)
results from the interactions of fast ions and ambient electrons; secondary electron bremsstrahlung
is produced by knock-on electrons accelerated in fast ion interactions (Hayakawa & Matsuoka
1964). Both of these processes lead to continuum X-ray emission. X-ray line emission results from
atomic de-excitations in the fast ions following electron capture (Silk & Steigman 1969; Watson
1976; Pravdo & Boldt 1975; Bussard, Ramaty, & Omidvar 1978) and in ambient ions following
inner-shell vacancy creation. The latter process has not yet been applied to astrophysics. Dogiel
et al. (1997) have recently considered the X-ray emission that should accompany the gamma-ray
line production in Orion. They have only considered the secondary electron bremsstrahlung and
concluded that the 0.5-2 keV emission that accompanies the observed gamma-ray line emission
from Orion will exceed the upper limits that they derived using ROSAT observations. We have
subsequently taken into account both continuum processes and line emission from de-excitations
in fast O (Ramaty, Kozlovsky, & Tatischeff 1997a) and showed that, even though the inverse
bremsstrahlung is more important than the secondary electron bremsstrahlung, the total X-ray
continuum emission from Orion is not inconsistent with the Dogiel et al. (1997) derived ROSAT
upper limit. On the other hand, we showed that a conflict may exist between that ROSAT upper
limit and the X-ray line emission following electron capture onto fast O nuclei. However, as we
suggested, this conflict could be resolved if the X-ray and gamma-ray lines are produced in an
ionized medium or if the current epoch accelerated particle spectrum is suppressed at low energies,
for example by energy losses.
In this paper we present detailed calculations of X-ray continuum and line production by
accelerated particle interactions. The bulk of our treatment is for a steady state, thick target model
with a neutral ambient medium. This is the standard model in which most of the gamma-ray
calculations have been carried out (e.g. Ramaty et al. 1996). But we have also investigated the
effects of an ionized ambient medium and a time-dependent model, as these modifications could
have important consequences on the predicted X-ray to gamma-ray production ratio. In our
treatment of the continuum, we have supplied the details of the calculations and we have improved
the employed cross sections, thereby confirming our previous preliminary results (Ramaty et al.
1997a). We have greatly expanded our treatment of X-ray line emission. We have investigated
– 4 –
in detail the atomic physics relevant to line emission from de-excitations in fast O, checking
our theoretical calculations against laboratory data whenever available. We then expanded the
treatment to the other abundant accelerated ions (C, N, Ne, Mg, Si, S and Fe), and we have
also calculated the X-ray line emission produced in ambient ions following inner-shell vacancy
creation by the accelerated particles. We have used the ROSAT all-sky survey (Snowden et
al. 1995) to derive the X-ray count rates from the Orion region that could be associated with
accelerated particle interactions; the implied fluxes are quite different from the upper limit given
by Dogiel et al. (1997). The unambiguous future detection of the predicted X-rays produced by
accelerated particles in Orion, and potentially elsewhere in the Galaxy, should provide important
new insights into the origin of the low energy cosmic rays whose presence in Orion is revealed by
the COMPTEL gamma-ray line observations.
2. Interaction model
We consider a steady state, thick target interaction model in which accelerated particles with
given energy spectra and composition are injected at a constant rate into an interaction region of
solar composition and produce atomic and nuclear reactions as they slow down to energies below
the thresholds of the various reactions. We perform the calculations in a neutral ambient medium.
In §5.1 we discuss the expected modifications for a partially ionized medium and in §5.2 the
modifications that could result if the accelerated particle population is allowed to evolve in time.
The thick target X-ray and gamma-ray production rates can be written as (e.g. Ramaty et
al. 1996)
Q =1
(1 + 1.8nHe
nH)mp
∑
ij
Ainj
nH
∫ ∞
0
σij(En)dEn
Z2i (eff)(
dEdx )p,H
∫ ∞
En
dNi
dt(E′
n)dE′n . (1)
Here i and j range over the accelerated and ambient particle types that contribute to the atomic
or nuclear product considered; En is the accelerated particle energy per nucleon; dNi
dt (En) is the
differential injection rate of projectiles of type i into the target region, measured in particles
(MeV/nucleon)−1s−1; σij(En) is the cross section for the particular reaction considered; (dEdx )p,His the proton energy loss rate per g cm−2 in ambient neutral H; Zi, Ai and cβi are the nuclear
charge, mass and velocity of projectiles of type i; Zi(eff) = Zi[1 − exp(−137βi/Z2/3i )] is the
equilibrium ionic charge in a neutral ambient medium (Pierce & Blann 1968); nH , nHe and nj are
the densities of ambient H, He and constituent j; and mp is the proton mass.
We perform calculations with an accelerated particle source spectrum of the form (Ramaty et
al. 1996)
dNi
dt(En) ∝ E−1.5
n e−En/E0 . (2)
The power law E−1.5n is appropriate for strong shock acceleration in the nonrelativistic region.
The exponential cutoff, introduced by Ellison & Ramaty (1985) for solar flare acceleration, could
– 5 –
be caused by a finite shock size or finite acceleration time. In the case of Orion, arguments of
energetics require a hard spectrum in the nonrelativistic region (Ramaty et al. 1996), such as
that given by equation (2) with as high a value for the turnover energy (E0<∼ 100MeV/nucleon)
as allowed by the requirement that the high energy gamma-ray emission due to pion decay not be
overproduced (Tatischeff, Ramaty, & Mandzhavidze 1997). While such values of E0 are reasonable
for solar flares, it is not clear that in the case of strong shock acceleration the relevant geometry
and time scales for Orion will lead to a cutoff at a sufficiently low energy. Alternatively, the
acceleration in the nonrelativistic region could be stochastic due to turbulence or an ensemble of
weak shocks (Bykov & Fleishman 1992; Bykov 1995). This mechanism predicts an even harder
nonrelativistic spectrum (E−1n ), and one which steepens at higher energies where the acceleration
is due to single weak shocks. Because of its simplicity, we shall use equation (2) in our subsequent
calculations, allowing E0 to vary from 10 to 100 MeV/nucleon.
We employ three different compositions for the accelerated particles: CRS and WC (Ramaty
et al. 1996, table 1); and OB (Parizot et al. 1997a, table 1 the OB/0.02 column). CRS is the
composition of the current epoch Galactic cosmic-ray sources, WC is the composition of the winds
of Wolf-Rayet stars of spectral type WC, and OB is the average composition of the winds from
OB associations. The C and O abundances relative to protons, α-particles and heavier metals are
much higher for the WC case than those for the CRS case. For the OB case, these abundances
ratios are intermediate between those of the CRS and WC cases.
3. X-ray continuum emission
Energetic ions produce continuum X-ray emission via both inverse bremsstrahlung (Boldt and
Serlemitsos 1969, hereafter IB) and bremsstrahlung from secondary knock-on electrons (see also
Anholt 1985). For nonrelativistic protons interacting in stationary H, the inverse bremsstrahlung
cross section is identical to the bremsstrahlung cross section for electrons of kinetic energy
(me/mp)E also interacting in stationary H; here me and mp are the electron and proton masses
respectively and E is the proton kinetic energy. We used equation 3BN from Koch and Motz
(1959). For heavier ions interacting in an ambient medium consisting of heavier atoms, we replaced
the proton energy E by the energy per nucleon of the projectile, En, and multiplied the cross
section by Z2i Zj , where Zi and Zj are the fast ion and ambient atom charge numbers, respectively.
The secondary electrons are knock-on electrons which subsequently produce bremsstrahlung
by interacting with the ambient atoms. The angle averaged differential X-ray production cross
section for secondary electron bremsstrahlung (SEB) can be written as
dσ
dǫ(En, ǫ) =
Z2i Z
2j
mp
∫ ∞
ǫ
dσBR
dǫ(Ee, ǫ)
dEe
(Aj
Zj)dEe
dx (Ee)
∫ ∞
Ee
dσKN
dEe(En, E
′e)dE
′e , (3)
where (dσKN/dEe)(En, E′e) is the knock-on cross section for the ejection of an electron of energy
E′e by a proton of energy En interacting with H (Chu et al. 1981 with corrections at high energies
– 6 –
from Rudd et al. 1966 and Toburen and Wilson 1972); (dσBR/dǫ)(Ee, ǫ) is equation 3BN of Koch
and Motz (1959) for electrons of energy Ee interacting with H and radiating a photon of energy ǫ;
and dEe/dx is the electron energy loss rate per g cm−2 in the ambient medium (Berger and Seltzer
1982). Since dEe/dx scales approximately as Zj/Aj , where Aj is the target atomic number, the
overall cross section scales as Z2i Z
2j . In comparison, the IB cross section scales as Z2
i Zj .
In Figure 1a we show our calculated IB and SEB cross sections for protons interacting in H
and Be, and compare our results for Be with experimental data (Chu et al. 1981). We see that
while for the Be target the two calculated cross sections are approximately equal, for the H target
the IB cross section dominates (except at the highest energies). This is the direct consequence of
the dependencies of the cross sections on the target charge number Zj derived above. In the case
of the Be target we get good agreement with the experimental data at 90◦, the discrepancy of less
than a factor of 2 possibly being due to our angle averaging and contaminations in the experiment,
for example Compton scattering of gamma rays in the Be target.
Using equation(1) we calculated the ratio of the IB and SEB productions as a function
of photon energy for an ambient medium with solar abundances, for various values of the
characteristic energy E0 [Eq. (2)], and various accelerated particle compositions. We find that,
as expected, the ratio is practically independent of the accelerated particle composition. We
thus show results only for the CRS composition (Figure 1b). We see that, except at the highest
energies, the IB-to-SEB ratio ranges from about unity to almost 10, depending on the photon
energy and the spectrum of the accelerated particles (i.e. the value of E0).
4. X-ray line emission
X-ray line emission results mainly from 2p to 1s and 3p to 1s transitions, in either the fast
ions or the ambient atoms, giving rise to Kα and Kβ X-rays respectively. In the case of the
fast ions, the 2p and 3p states can be populated either by electron capture from ambient atoms
(i.e. charge exchange) or by excitation of 1s electrons for ions having one or two electrons. We
neglected the Kα and Kβ X-ray production from fast ions having more than two electrons as the
collision energy in this case is mostly given to the outer electrons and thus not giving rise to a
significant K-shell electron excitation. The fast ions also produce K-shell vacancies in the ambient
atoms (Garcia, Fortner, & Kavanagh 1973; Cahill 1980). We first consider the K X-ray production
in fast O.
4.1. K X-rays from fast oxygen
X-ray line production from fast O has already been treated by Pravdo & Boldt (1975) and
Watson (1976). The latter has considered the interaction of energetic O with only ambient
hydrogen. But, as shown by Bussard et al. (1978) for Kα X-ray emission from fast Fe, heavier
– 7 –
ambient elements cannot be neglected despite their lower abundances because of the strong
dependence of the charge-exchange cross section on the charge of the target nucleus. Pravdo &
Boldt (1975) have taken into account the contributions of the heavier elements, but as we shall see,
their use of the Oppenheimer-Brinkman-Kramers (OBK) approximation for the charge-exchange
cross section in the form presented by Schiff (1954) gives a poor description of the available
experimental data.
The main lines produced by fast O ions result from the 2p to 1s transitions in H- and
He-like projectiles giving rise to Kα X-rays at 0.65 keV (O VIII line) and 0.57 keV (O VII line),
respectively (Matthews et al. 1973). In addition, we considered the 3p to 1s transitions, which
give rise to non-negligible Kβ X-rays at 0.77 and 0.67 keV, for H- and He-like O ions, respectively
(Hopkins et al. 1974).
4.1.1. Charge Exchange cross section
Even though the OBK cross section is known to exceed the experimental data by a factor
of 10 or more in certain cases, it predicts quite accurately the shape of the measured cross
sections versus energy (e.g. the review of Belkic, Gayet, & Salin 1979). Schiff (1954) has derived
a general form for the OBK cross section for capture of electrons by fast ions from the ground
state of a H-like ion. This formula is not appropriate to describe electron capture from heavy
targets containing many atomic electrons. Nikolaev (1967) has extended the OBK cross section to
heavy ion charge exchange, taking into account the complete atomic configuration of the target
atoms. He also derived a semi empirical scaling relation in order to adapt his theoretical result to
experimental data. But subsequent measurements have shown that a discrepancy of a factor of 2-3
remains between theory and experiment in some cases (e.g. Ferguson et al. 1973). Thus, instead
of using the Nikolaev (1967) semi empirical factor, we normalized the Nikolaev cross section to
experimental data. In the Nikolaev formalism we used the binding energies of the target electrons
from Sevier (1979), and the Slater (1930) rules to take into account the external screening of the
nuclear charge by the inner shells.
A compilation of experimental cross sections is shown in Figure 2, together with theoretical
calculations. The closed symbols show K X-ray production cross sections due to charge exchange
for fast fully stripped O and F interacting with neutral H, He, Ar and Kr. The solid curves are
our fits to these data obtained by using the Nikolaev (1967) formalism to calculate the capture
cross sections σn≥2 to all states with principal quantum number n ≥ 2. To take into account the
captures which populate the 2s metastable state (which does not lead to K X rays), we reduced
σn≥2 by 4% based on the calculations of Guffey, Ellsworth & Macdonald (1977) for O and F
projectiles in He. This small correction, however, is negligible in comparison with the overall
normalizing factor of 0.1 that we applied to the calculated curves to fit the data. The open
symbols show the total electron capture cross section from the charge spectrometer experiment of
Macdonald et al. (1972) for fluorine-nitrogen collisions. The dashed curve is our fit to these data,
– 8 –
again using the Nikolaev (1967) formalism but with a sum over all n≥1, and the same normalizing
factor of 0.1. It is encouraging that with a single normalizing factor we could account for all of the
data in Figure 3 with accuracy better than a factor of 2. In addition, the normalizing factor of
0.1 is within the range of the Nikolaev semiempirical normalizations for charge exchange on fast
protons.
We also compared the predictions of the Schiff (1954) formula with the data shown in Figure 2.
While for the H target, the formula gives an acceptable fit with the same normalization of 0.1, it
predicts incorrect spectral dependencies for targets heavier than He, which is not surprising since
the formula was developed for H-like targets in the ground state.
4.1.2. Excitation cross section
The plane-wave-Born-approximation (PWBA) gives a satisfactory description for the Coulomb
excitation of atomic electrons (Bates 1962). Figure 3 shows a comparison of theoretical cross
sections with the experimental data of Hopkins, Little, & Cue (1976a) for the excitation of 1s
electrons which leads to K X-ray emission. The theoretical curves consist of the sum of the 1s→2p
and 1s→3p excitation cross sections, excitations to higher levels, which have much smaller cross
sections, being neglected. The cross sections for the excitation of F7+ are greater than twice those
of F8+ (F7+ has two K-shell electrons which could be excited), because we took into account
the screening of the nuclear charge of the projectile by the other K-shell electron. Although the
PWBA theory indicates that the excitation cross sections scale as the target charge squared,
the Hopkins et al. (1976a) measurements show that the cross sections for excitation by He are
∼20% lower than four times the corresponding ones for excitation by H. This discrepancy was
attributed to the screening effect of the helium electrons (Hopkins et al. 1976a). To take this
effect into account, we used a normalization factor of 0.8 for all the target elements heavier than
hydrogen in addition to the scaling with the target charge squared. This approximation has only
a small impact on the final result, since the contribution of the elements heavier than He to the
excitation represents less than 4% of the final X-ray production. We neglected the contributions
of excitation reactions in which both the projectile and the target are excited based on the results
of Moiseiwitsch & Stewart (1954).
4.1.3. Equilibrium charge fractions
The O ions lose energy more slowly than they capture and lose electrons by interacting with a
neutral ambient medium of solar composition (see the discussion of Bussard et al. 1978 for fast Fe
ions). Thus, in a steady state, the charge fractions Fn, where n is the number of bound electrons
of the projectile, satisfy the equation
Fnσ(n)c = Fn+1σ
(n+1)I , (4)
– 9 –
where σ(n)c and σ
(n)I are, respectively, the electron capture and ionization cross sections for O
ions with n electrons interacting with an ambient medium of solar composition. Ionization cross
sections scale approximately as the target charge squared (Rule 1977). Thus, because of the low
abundances of the heavier elements (Anders & Grevesse 1989), the fast ions lose their electrons by
colliding mainly with ambient H and He. This is not the case for electron captures because of the
strong dependence of the charge exchange cross section on the charge of the target nucleus (e.g.
Figure 2). We took into account the ambient H, He, C, N, O, Ne, Mg, Si, S and Fe to calculate
the total electron capture of the fast O ions in the medium of solar composition. Ionization cross
sections of O ions in collisions with neutral H and He were taken respectively from Watson (1976)
and Rule (1977). The electron capture and loss cross sections for fast O in a medium of solar
composition are shown in Figure 4a and the F0, F1 and F2 charge fractions determined from
equation (4) are shown in Figure 4b. We see that contrary to the charge exchange cross sections,
the ionization cross sections have a weak energy dependence. As most of the X-ray line emission
is produced near the energy at which the charge exchange and ionization cross sections are equal,
and because of the weak energy dependence of the ionization cross sections, the final X-ray line
production is not very sensitive to the exact magnitude of the charge exchange cross section. We
found that an uncertainty of a factor of 2 in the charge exchange cross section (§4.1.1) leads to
only a 25% uncertainty in the X-ray emissivity.
4.1.4. K X-ray multiplicities
The multiplicities of the H-like (O VIII) and He-like (O VII) Kα lines produced by a fast O of
initial energy En0 slowing down in a medium with solar abundances due to interactions with the
ambient constituent j of abundance nj/nH can be obtained from equation (1),
MO VIII(j) =Ai
(1 + 1.8nHe
nH)mp
( nj
nH
)
∫ En0
0
dEn
Z2i (eff)(
dEdx )p,H
(
F0σ(0)c;j (2p) + F1σ
(1)ex;j(1s → 2p)
)
(5)
and
MO VII(j) =Ai
(1 + 1.8nHe
nH)mp
( nj
nH
)
∫ En0
0
dEn
Z2i (eff)(
dEdx )p,H
(
F1σ(1)c;j (2p) + F2σ
(2)ex;j(1s → 2p)
)
. (6)
Here the Fn are the charge fractions of the O ions; σ(n)c;j (2p) is the electron capture cross section
into the 2p level, either directly or following a cascade, by an ion which already has n electrons
from the target element j; σ(n)ex;j(1s → 2p) is the 1s→2p excitation cross section for an O ion having
n electrons by the target element j. The O Kβ X-ray multiplicities are obtained by replacing 2p
by 3p in equations (5) and (6).
To calculate σ(n)c;j (2p) and σ
(n)c;j (3p), we first calculated the total K X-ray production as in
§ 4.1.1, and then used the experimental result of Hopkins et al. (1974) to determine the relative
contributions of the Kα and the Kβ lines. Hopkins et al. (1974) measured the K X-ray production
– 10 –
from fully stripped O of 1.9 MeV/nucleon interacting with various targets. As the projectiles were
initially devoid of electrons, the detected K X-ray emission could have arisen only from electron
capture. They found that, independent of the target charge, about 60% of the total K X-ray
production was in the Kα line and 20% in the Kβ line, the remaining 20% coming from the rest
of the series. Combining this result with the calculation of σ(n)ex;j(1s → 2p) and σ
(n)ex;j(1s → 3p), we
eventually found that each of the two Kβ lines, i.e. from the H- and He-like O, represents 1/4 of
the corresponding Kα line.
We have evaluated equations (5) and (6) and the results are given in Tables 1 and 2, where
we have separated the contributions from electron captures and excitations of 1s electrons. The
multiplicities are independent of the initial O energy for En0>∼ 10 MeV/nucleon, because at these
high values of En0 the nuclei are fully stripped and the probability for capturing electrons is very
small. The results of Tables 1 and 2 can be compared with the multiplicities given by Pravdo &
Boldt (1975). Although our results for the contribution of charge exchange are ∼4 times lower
than theirs, the total Kα X-ray production is only 1.8 times lower. This is because excitation is
now seen to be the dominant mechanism. This result is supported by the accelerator measurement
of Hopkins et al. (1976a), which provides a clear signature that excitation is the dominant process
of K X-ray production for 1-3 MeV/nucleon F7+ and F8+ projectiles in hydrogen and helium.
The same conclusion was found also by Bussard et al. (1978) for the Kα X-ray emission from
fast Fe. In particular, we can see from Table 2 that the excitation contribution to the O VII line
production, which was not taken into account by Pravdo & Boldt (1975), represents 60% of the
total multiplicity.
Using Equations (5) and (6) we can also evaluate the differential multiplicities∑
j dMO VIII(j)/dEn0 and∑
j dMO VII(j)/dEn0, i.e. the number of photons produced by
the projectile, due to interactions with all the constituents of the ambient medium, as it slows
down over the differential energy interval dEn. The results for O are shown in Table 3 and
Figure 5c. Similar multiplicities for C, N, Ne, Mg, Si, S and Fe are also shown in Tables 3 and 4
and in Figures 5 and 6. These multiplicities are discussed below. We see that for O the differential
multiplicities peak around 1 MeV/nucleon and fall off rapidly at both lower and higher energies.
The differential multiplicities for O can be compared with the results of Pravdo & Boldt (1975).
The positions of the peaks are consistent although, as already discussed, the magnitudes of the
multiplicities are lower.
4.2. K X-rays from the other fast ions
The major X-ray lines from the fast ions are given in Table 5. We used the same formalisms
for the charge exchange and the excitation cross sections as described for O. In particular, we used
for the charge exchange cross sections the same normalization factor of 0.1 for all the projectiles
and targets (§ 4.1.1). We checked our charge exchange calculations with the experimental data of
Berkner et al. (1977) for 3.4 MeV/nucleon Fe projectiles in charge states +20 to +25 interacting
– 11 –
with H2 and found agreement within 40%. For the ionization cross sections, we used the scaling
relation (Rule 1977)
σZi
I (vi) = (8/Zi)4σ8
I (8vi/Zi) , (7)
where vi and Zi are the speed and charge of the projectile, and σ8I is the ionization cross section of
fast O ions in an ambient medium of solar composition (§4.1.3, and Figure 4a). We assumed for
all the fast ions that the Kα and the Kβ lines represent respectively 60% and 20% of the K X-ray
production from electron capture.
The results for the Kα differential multiplicities, along with the total multiplicities, are shown
in Figures 5 and 6. As for O, we found that the multiplicities for the Kβ photons are approximately
1/4 of the corresponding Kα multiplicities. The multiplicities decrease with increasing projectile
charge, from a total multiplicity of 87 photons/projectile for C to 7 photons/projectile for Fe. The
projectile energies at which the differential multiplicities peak increase with increasing projectile
charge. Our results for Fe are in good agreement with the previous calculations of Bussard et al.
(1978). In particular, we agree that excitation of 1s electrons is the dominant mechanism of Kα
X-ray production, that ambient O and Fe are the main contributors to electron capture by fast Fe
ions and that the peak of the X-ray line production from fast Fe is at ∼9 MeV/nucleon. Both
calculations of the total emissivity of Fe Kα lines agree within 20% (see the table 2 and the notes
added in the manuscript of Bussard et al. 1978).
4.3. K X-rays from the ambient atoms
The K X-ray line emission from the ambient atoms results from the filling of inner-shell
vacancies produced by the fast ions. In the case of proton impact, the line energies correspond to
the difference of the orbital energies, because both the vacancy production and the subsequent
filling of the vacancy occur in times short compared to the relaxation times for the atomic wave
functions (Garcia et al. 1973). For heavy-ion collisions, the lines could be shifted by several tens
of eV, significantly broadened and slitted up into several components, due to multiple inner-shell
plus outer-shell simultaneous ionizations (Garcia et al. 1973). We have not taken into account
these effects, although we believe that they could provide interesting constraints on the accelerated
particle composition through fine spectroscopy. We considered the Kα and Kβ lines from ambient
C, N, O, Ne, Mg, Si, S, Ar, S and Fe and have determined the transition energies (Table 6) from
the atomic electron binding energy tables of Sevier (1979). We do not consider Kβ X-rays from C,
N, O, Ne and Mg, as these atoms in their ground state do not have 3p electrons.
The X-ray line production cross section can be written as
σX = σIwk, (8)
where σI is the cross section for the collisional ionization leading to the K-shell vacancy, w is the
fluorescence yield for the K shell (Krause 1979) and k is the relative line intensity among the
– 12 –
possible transitions which can fill the inner-shell vacancy (Salem, Panossian, & Krause 1974).
For proton impact, we calculated the ionization cross sections from the semiempirical formula of
Johansson & Johansson (1976), with an extrapolation at high energy from appendix 2 of Garcia
et al. (1973). For heavier projectiles, we assumed a Z2i dependence, as predicted by both the
PWBA and the impulse approximation theories. This assumption gives a poor description of the
available experimental data at low energies due to molecular effects, but becomes reasonable as
the cross section reaches its maximum, i.e. for En ≃ (mp/me)uK (in MeV/nucleon), where uK is
the binding energy of the K shell (Garcia et al. 1973).
K X-ray production cross sections for fast protons colliding with C, O, Si and Fe are shown
in Figure 7. The Kα line production cross sections do not show a strong dependence on the target
charge even though the ionization cross section varies as Z−4j (Johansson & Johansson 1976),
because this variation is partially compensated by the Z3.25j dependence of the fluorescence yields
up to Fe (Krause 1979).
5. Results and Applications for Orion
We developed a code for the calculation of the X-ray emission resulting from the various
continuum and line producing processes discussed above. The code allows the use of various
accelerated particle energy spectra and compositions in a steady state, thick target model. The
ambient medium is assumed to be neutral with a solar composition. We discuss in § 5.1 the
modifications that would result for X-ray production in a partially ionized medium and in §5.2
those for a time-dependent model. We took into account the photoelectric absorption of the
X-rays, again using solar abundances, and the cross sections of Morrison & McCammon (1983).
We present results normalized to the accompanying 3-7 MeV nuclear gamma-ray line emission
which we calculated as in Ramaty et al. (1996).
The calculated X-ray fluxes, normalized to a 3-7 MeV nuclear gamma-ray flux of 10−4 photons
cm−2 s−1 (the approximate value of the observed gamma-ray line emission from Orion), are
shown in Figures 8 and 9 for the CRS and WC compositions, respectively. We took into account
photoelectric absorption using NH=3×1021 cm−2, our estimate for the H column density towards
Orion. We estimated this column density from the HI survey of Heiles & Habing (1974) and the
CO map of Dame et al. (1987), together with a CO-to-H2 conversion factor of (1.06±0.14)×1020
cm−2 (K km s−1)−1 (Digel et al. 1995).
We first note that the continuum emission is indeed dominated by the inverse bremsstrahlung
(§ 3). We have calculated the SEB differential luminosity for E0=30 MeV/nucleon without
including the photoelectric absorption and compared the results with those given in figure 1 of
Dogiel et al. (1997). For the CRS composition our results are lower than theirs by factors of 19,
6.6 and 1.9 at Ex=0.2, 1 and 10 keV, respectively; for the WC composition, the discrepancy is
even larger, the corresponding factors being 75, 31 and 9. The discrepancy is due, in part, to the
– 13 –
approximate normalization to the nuclear gamma-ray line emission used by Dogiel et al. (1997).
However, by repeating their calculation using the same formalism and input data (Hayakawa
1969), we find results which agree with our more accurate approach but which are lower than that
of Dogiel et al. (1997) by about an order of magnitude at 1 keV.
We calculated the width of the lines produced by the fast ions assuming an isotropic angular
distribution for these particles. We see that below about 1 keV the X-ray emission is dominated
by these lines, in particular the lines from fast C and O. For the much narrower lines from the
ambient atoms, we assumed delta functions at the nominal line energies (Table 6) and plotted the
spectra in 10 eV bins. The most prominent narrow line is that at 6.4 keV from ambient Fe. The
width of the lines resulting from de-excitations in the fast ions are quite broad. For example, the
O lines, which are produced around 1 MeV/nucleon, have widths of about 0.06 keV (FWHM).
This large width distinguishes them from the X-ray lines produced in a hot plasma.
By comparing Figures 8 and 9, we see that the line-to-continuum ratio below 1 keV is lower
for the CRS composition than for the WC composition because of the additional bremsstrahlung
from the protons and α-particles. The line-to-continuum ratio below 1 keV is also lower for the
higher E0, because the fast ions produce line emission only at the low energies (Figures 5 and 6).
The X-ray emission at high energies ( >∼ 10 keV) is very sensitive to the value of E0.
In Figures 10 and 11 we compare the expected X-ray fluxes from Orion with the diffuse
extragalactic X-ray background. We calculate the X-ray emission for the CRS composition with
E0=100 MeV/nucleon and for the WC composition with E0=20 MeV/nucleon. We consider two
cases: uniform gamma-ray emission from the box [201◦≤lII≤217.5◦, -21◦≤bII≤-9◦] which contains
almost all of the 3-7 MeV emission observed with COMPTEL, (12.8±1.5)×10−5 photons cm−2
s−1 (Bloemen et al. 1997); the hot spot observed with COMPTEL at lII=213.6◦, bII=-15.7◦
from which the 3-7 MeV emission flux is (3.3±0.8)×10−5 photons cm−2 s−1 (H. Bloemen, private
communication, 1996). As the size of the spot is not well known, we considered a 9 degree2 box
[212.25◦≤lII≤215.25◦, -17.25◦≤bII≤-14.25◦] which represents the approximate extent of the hot
spot in the published COMPTEL map (Bloemen et al. 1997). We took the extragalactic diffuse
X-ray background from Gendreau et al. (1995) below 10 keV and from Gruber (1992) at higher
energies. We increased the Gruber (1992) data by 9% to achieve a smooth transition to the
Gendreau et al. (1995) data.
Considering first the X-ray continuum at high energies, we see that if the gamma-ray source
is uniformly spread over the entire 200 degree2 box (Figures 10a and 11a), it will be very difficult
to observe these X-rays because the predicted emission is much lower than the extragalactic
background. In the case of the 9 degree2 hot spot, the chances of detecting the high energy X-ray
continuum above the extragalactic background are better, in particular for the CRS composition
with E0=100 MeV/nucleon (Figure 10b) which yields the highest X-ray continuum for a given
nuclear gamma-ray flux. On the other hand, the predicted line emission, in particular the lines
from fast O, exceeds the extragalactic background independent of the spectrum and composition
– 14 –
of the accelerated particles.
ROSAT observations can be used to test our predictions of the expected line emission below 2
keV. We used the ROSAT all-sky survey (Snowden et al. 1995) to compare our calculations with
the observed count rate in the ROSAT R45 energy band, i.e. from 0.47 to 1.2 keV (Snowden et
al. 1994). We considered the same two source regions as in Figures 10 and 11: the 200 degree2
box for which we assume a uniform gamma-ray emission; and the 9 degree2 gamma-ray hot spot.
For the 200 degree2 box ROSAT/PSPC detected a total of 70.1 counts s−1 in the R45 band.
We subtracted the contributions of the Orion nebula region and the Ori OB1 association, which
were interpreted as thermal emission most likely from T Tauri type stars (Yamauchi, Koyama, &
Inda-Koide 1994; Yamauchi et al. 1996). The remaining count rate of 60.6 counts s−1 is plotted
in Figure 12a. For the 9 degree2 hot spot there are 2.7 counts s−1 in the ROSAT/PSPC R45 band
(Figure 12b).
In the 200 degree2 box, the corresponding X-ray luminosity is ∼2×1034 ergs s−1 assuming a
distance to Orion of 450 pc. This luminosity is 20 times greater than the upper limit derived by
Dogiel et al. (1997), even though our value pertains to the 0.47-1.2 keV range whereas that of
Dogiel et al. (1997) is for X-rays between 0.5 and 2 keV. We believe that the discrepancy is due to
the fact that Dogiel et al. (1997) searched for only nonthermal continuum whereas we considered
all the emission that could not be related to known sources in Orion (see above). In particular,
because of the presence of the lines (Figures 8 and 9), the total X-ray emission from low energy
particle interactions may look similar to thermal emission (Raymond & Smith 1977) given the
rather poor energy resolution of ROSAT/PSPC.
Also shown in Figure 12 are the predicted R45 count rates obtained by convoluting the
calculated X-ray spectra with the ROSAT/PSPC response function (Snowden et al. 1994) and
taking into account photoelectric absorption with the same H column density of 3×1021 cm−2
for the two source regions. The results, normalized to the gamma-ray intensities, are given as
functions of the characteristic energy E0 [Eq. (2)] for the CRS, OB and WC compositions. The
count rates due to extragalactic background were obtained in the same manner, i.e. by convoluting
the spectrum given by Gendreau et al. (1995) with the ROSAT/PSPC response function and using
the same H column density for the photoelectric absorption as for the two Orion source regions.
In Figure 12 the increase of the predicted count rates as the accelerated particle spectrum
becomes softer (i.e. with decreasing E0) is due to the decrease of the gamma-ray production
relative to the X-ray production, which occurs at much lower energies than the gamma-ray
production. The CRS composition provides the lowest X-ray emission because of its highest
proton and α-particle abundances relative to those of 12C and 16O. Indeed, accelerated protons
and α-particles produce 3-7 MeV emission while interacting with ambient CNO, but no significant
X-ray line emission in the ROSAT energy range. We note that the extragalactic X-ray background
accounts for only 1/6 of the observed count rates in both Figures 12a and 12b. We see in
Figure 12a that except for the very low E0, the calculated count rates are lower than the observed
– 15 –
rate, suggesting a contribution of other sources, for example T Tauri stars. On the other hand, we
see in Figure 12b that the predicted X-ray counterpart of the observed nuclear gamma-ray line
emission from the 9 degree2 hot spot exceeds the ROSAT count rate except at the highest allowed
values of E0 near 100 MeV/nucleon. This discrepancy could be mitigated by assuming that the
area of the gamma-ray hot spot is larger than 9 degree2, although for a smaller area a more severe
discrepancy would ensue. The discrepancy could be resolved if the X-rays and gamma rays are
produced by accelerated particles interacting in a partially ionized medium, for example at cloud
boundaries (Bykov & Bloemen 1994; Ramaty et al. 1997a,b; Kozlovsky et al. 1997; Parizot et
al. 1997a), or in a time-dependent model in which the spectrum of the accelerated particles has
become quite flat because of energy losses. We elaborate on these two effects in the next two
subsections.
5.1. Modifications due to a partially ionized ambient medium
We consider the effects of a partially ionized ambient medium on the K X-ray production in
the ROSAT R45 energy band (0.47 to 1.2 keV). In this energy range, the K X-rays are produced
by fast C, N, O and Ne. As the nature of the cosmic ray ionization at the cloud boundaries is not
well understood, we assume for simplicity that the ambient H and He are fully ionized but that
the heavier ambient elements remain essentially neutral. Thus the fast ions capture electrons from
ambient C and heavier atoms only. As the capture cross sections increase rapidly toward lower
energies while the electron loss cross sections are essentially constant (Figure 4a), the charge state
distribution of the fast ions in an ionized medium is quite similar to that in a neutral medium
(Figure 4b), except that it is established at lower values of En. Consequently, K X-rays are also
produced at lower energies (about 0.1-1 MeV/nucleon for the C, N, O and Ne K X-rays) in an
ionized medium than in a neutral medium. Although the fast ions do not capture electrons from
ambient H and He, the rate of electron capture is not very different from that in a neutral medium
because of the more efficient electron capture from heavier ambient atoms caused by the increase
of the capture cross sections toward lower energies (Figure 4a). We also do not expect substantial
reductions of the magnitude of the K X-ray multiplicities due to excitation, because the excitations
are mainly due to the ambient nuclei and the cross sections are only slowly decreasing at lower
energies (Figure 3).
The main difference between K X-ray production from fast ions interacting in an ionized or
a neutral medium is due to the energy losses. It is well-known that fast ions lose more energy in
a plasma than in a neutral medium, because the collective long-range Coulomb interactions are
more efficient than ionization. Both the X-ray and gamma-ray production rates are reduced, but
as we shall see, the effect is stronger for the X-rays.
The energy loss rate depends on the effective charge of the fast ion. We calculated the
effective charge of a fast O in a medium of solar composition in which H and He are fully ionized
and the result is shown by the dashed curve in Figure 13a. We found that this effective charge
– 16 –
could be approximated by a formula similar to that used to describe the effective charge in a
neutral medium (§2),
Zi(eff) = Zi[1− exp(−220βi/Z2/3i )], (9)
with a modified exponential to take into account the increase of the fast ion charge in the ionized
medium. We then calculated the O ion energy loss in a plasma using equations (4.21) and
(4.22) from Mannheim and Schlickeiser (1994), in which we substituted the nuclear charge of the
projectile by its effective charge [Eq. (9)]. We assumed a typical temperature of 104 K at cloud
boundaries. The energy loss is not very sensitive to temperature for En ≥ 0.1 MeV/nucleon.
In Figure 13b we show the ratio of the energy loss in an ionized medium to that in a neutral
medium for fast O ions. We see that while at high energies the increase in the energy loss rate
is about a factor of 2, below an MeV/nucleon the energy loss rate in an ionized medium exceeds
that in a neutral medium by more than a factor of 6. This result is supported by the laboratory
measurements of Hoffmann et al. (1994) for the energy loss of various fast ions in a hydrogen
plasma.
Because the X-ray line emission is produced between about 0.1 and 1 MeV/nucleon, while
the 3-7 MeV gamma-ray line production occurs essentially above 10 MeV/nucleon (Ramaty et al.
1996), the ratio of thick target [Eq. (1)] X-ray to gamma-ray line production in an ionized medium
will be lower than in a neutral medium, by about a factor of 3. We emphasize that this decrease is
mainly due to the increase in the fast ion energy loss rate rather than the changes in the electron
capture, ionization and excitation.
5.2. Modifications due to a time-dependent accelerated particle population
Because the K X-ray production in the ROSAT R45 energy band (0.47 to 1.2 keV) is due to
very low energy ions, time-dependent effects could significantly reduce the number of such ions
relative to that of the higher energy gamma-ray line producing ions, thereby decreasing the X-ray
production rate relative to the gamma-ray production rate.
To illustrate the effect, we first calculate the differential equilibrium particle number Y (E) for
steady state, thick target interactions. This is given by (see Eq. 1)
Y (E) =(dE
dt
)−1∫ ∞
E
dN
dt(E′)dE′ . (10)
where the energy loss rate in a neutral medium is
(dE
dt
)
= (1 + 1.8nHe
nH)mpnHv
Z2(eff)
A
(dE
dx
)
p,H
. (11)
The dashed curve in Figure 14 shows this Y (E) for O ions with E0=30 MeV/nucleon, normalized
such that the instantaneous energy deposition rate, 16∫∞
0 Y (E)(dE/dt)dE, is 1038 erg/s for an
– 17 –
average ambient hydrogen density of 10 cm−3. This is the approximate energy deposition rate
that accompanies the gamma-ray production rate in Orion due to O ions (Ramaty et al. 1996).
While the energy deposition rate can be calculated independent of the ambient density, the
equilibrium number does depend on the density which is quite uncertain. The value of 10 cm−3 is
not unreasonable if the accelerated particles spend part of their life time in the clouds.
Next we assume that the accelerated particles are injected as a delta function in time (i.e.
over a time interval which is very short compared to the life time against energy losses). The
time-dependent differential particle number is then given by (e.g. Parizot et al. 1997b)
Y (E, t) =dE′/dt
dE/dtQ(E′) . (12)
Here
t =
∫ E′
E
[dE
dt(E′′)
]−1dE′′ (13)
is the elapsed time since the injection of the particles and the energy loss rates in equation (12)
are derived at E′ and E. We normalize the injection source Q(E) such that the total energy
deposited at t=0 in the time-dependent case equals the deposited steady state energy over a time
period of 105 years. This leads to a total deposited energy in O nuclei of 3.2×1050 ergs. This
value, together with the contributions of the other accelerated nuclei, yields a total accelerated
particle energy content of about 1051 ergs (depending on the assumed composition), which could
have been supplied by the supernova that is thought to have occurred about 80,000 years ago and
reheated the Orion-Eridanus bubble (Burrows et al. 1993).
The results are shown by the solid curves in Figure 14 for the same ambient density and E0 as
used for the steady state result. We see that, as time progresses, the differential number densities
at low energies are suppressed relative to those at higher energies. Since in a neutral medium
the K X-ray line emission from O is typically produced around 1 MeV/nucleon while the gamma
rays are produced above 10 MeV/nucleon, we expect a significant reduction of the X-ray line to
gamma-ray line production ratio relative to the corresponding production ratio for the steady
state case. At t=3×104 years, for example, the reduction is about an order of magnitude.
6. Conclusions
We have investigated all the processes that lead to X-ray production by low energy cosmic
rays for a variety of accelerated particle compositions and energy spectra. We demonstrated
that the dominant continuum producing process is inverse bremsstrahlung produced by fast ions
interacting with ambient electrons. In addition, there is also a significant contribution from the
bremsstrahlung produced by secondary knock-on electrons. However, below a few keV the total
X-ray emission produced by accelerated ions is dominated by relatively broad line emission (line
– 18 –
widths δE/E≃0.1) resulting from de-excitations in the fast ions following electron captures and
excitations. In addition, accelerated particle interactions also produce much narrower X-ray lines,
due to inner-shell vacancy creation. The most prominent of such line is that at 6.4 keV from
ambient Fe.
We have calculated the X-ray line and continuum emission produced by the accelerated
particles in Orion which are thought to be responsible for the nuclear gamma-ray line emission
observed with COMPTEL (Bloemen et al. 1994, 1997). By first comparing the results with the
extragalactic diffuse X-ray background, we found that while the continuum is generally below
this background, the line emission from about 0.5 to 1.5 keV exceeds the background for all
the combination of parameters that we considered. We wish to point out that there could be a
significant contribution to the ∼0.5-1.5 keV diffuse X-ray background from as-yet unknown sources
within our Galaxy (e.g. Park et al. 1997), leaving the possibility that a substantial fraction of the
observed X-ray intensity in this energy range results from low energy cosmic ray interactions.
We have also compared our results with ROSAT observations of Orion in the 0.47 to 1.2 keV
energy band, again normalizing the X-ray emission to the observed gamma-ray emission. We found
that there is no conflict between the predicted total X-ray emission (lines and continuum) and the
data for a broad range of parameters if the gamma-ray line emission is uniformly distributed over
the entire molecular cloud complex. This conclusion differs from our previous one (Ramaty et al.
1997a) because of a lower predicted X-ray line emission, resulting from improved atomic physics
input, and because our estimated ROSAT flux from Orion is higher than the upper limit given by
Dogiel et al. (1997). However, the COMPTEL data show significant spatial structure. We found
that for the most prominent hot spot in the COMPTEL map, the standard thick target, steady
state interaction model, with a neutral ambient medium, predicts X-ray fluxes which exceed the
ROSAT data for a broad range of parameters. But the calculations could be consistent with the
data for any one, or a combination of the following possibilities: a very hard accelerated particle
spectrum; a partially ionized ambient medium; and a time-dependent accelerated particle energy
spectrum resulting from essentially instantaneous acceleration some tens of thousand of years ago.
There are as-yet no astrophysical X-ray observations that would unambiguously indicate an
origin resulting from low energy, accelerated ion interactions. Our calculations show that the most
promising signatures are the relatively broad lines between 0.5 and 1.5 keV, mainly the lines from
fast O, and that a promising target is the Orion region where the presence of such accelerated
particles is known from gamma-ray line observations.
We acknowledge K. Omidvar for discussions on the atomic processes leading to X-ray line
production. V. T. acknowledges an NRC-NASA/GSFC Research Associateship.
– 19 –
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This preprint was prepared with the AAS LATEX macros v4.0.
– 23 –
Table 1. Multiplicity of O VIII line X-rays
Elements Electron capture Excitation Totals
H 1.9 8.1 10.0
He 4.0 2.2 6.2
C 0.43 7.1·10−2 0.50
N 0.15 3.1·10−2 0.18
O 1.2 0.31 1.5
Ne 0.23 7.3·10−2 0.30
Mg 0.11 3.4·10−2 0.14
Si 0.14 4.3·10−2 0.18
S 8.8·10−2 3.0·10−2 0.12
Fe 0.21 0.14 0.35
Totals 8.5 11.0 19.5
Table 2. Multiplicity of O VII line X-rays
Elements Electron capture Excitation Totals
H 4.1 12.4 16.5
He 6.8 3.4 10.3
C 0.24 0.11 0.34
N 7.2·10−2 4.6·10−2 0.12
O 0.59 0.47 1.1
Ne 0.14 0.11 0.25
Mg 6.7·10−2 5.0·10−2 0.12
Si 7.6·10−2 6.4·10−2 0.14
S 4.1·10−2 4.4·10−2 8.5·10−2
Fe 0.10 0.21 0.32
Totals 12.2 16.9 29.2
– 24 –
Table 3. Multiplicity of C, N, O and Ne Kα lines
∆E C N O Ne
(MeV/nucleon) H-like He-like H-like He-like H-like He-like H-like He-like
0.1 - 0.2 0.25E-03 0.42E+00 - 0.23E-01 - 0.13E-02 - -
0.2 - 0.3 0.19E-01 0.37E+01 0.54E-03 0.45E+00 - 0.44E-01 - 0.52E-03
0.3 - 0.4 0.21E+00 0.90E+01 0.12E-01 0.21E+01 0.56E-03 0.35E+00 - 0.73E-02
0.4 - 0.5 0.92E+00 0.12E+02 0.87E-01 0.45E+01 0.67E-02 0.12E+01 - 0.47E-01
0.5 - 0.6 0.22E+01 0.11E+02 0.33E+00 0.62E+01 0.37E-01 0.23E+01 0.33E-03 0.17E+00
0.6 - 0.7 0.35E+01 0.79E+01 0.80E+00 0.67E+01 0.12E+00 0.33E+01 0.20E-02 0.42E+00
0.7 - 0.8 0.42E+01 0.48E+01 0.14E+01 0.60E+01 0.30E+00 0.39E+01 0.77E-02 0.77E+00
0.8 - 0.9 0.41E+01 0.26E+01 0.20E+01 0.46E+01 0.56E+00 0.40E+01 0.22E-01 0.11E+01
0.9 - 1.0 0.35E+01 0.13E+01 0.24E+01 0.31E+01 0.88E+00 0.36E+01 0.51E-01 0.15E+01
1.0 - 1.5 0.88E+01 0.13E+01 0.96E+01 0.47E+01 0.68E+01 0.87E+01 0.13E+01 0.88E+01
1.5 - 2.0 0.26E+01 0.87E-01 0.40E+01 0.41E+00 0.48E+01 0.14E+01 0.33E+01 0.50E+01
2.0 - 2.5 0.10E+01 0.12E-01 0.17E+01 0.62E-01 0.24E+01 0.23E+00 0.31E+01 0.16E+01
2.5 - 3.0 0.50E+00 0.29E-02 0.84E+00 0.15E-01 0.12E+01 0.56E-01 0.21E+01 0.49E+00
3.0 - 3.5 0.28E+00 0.89E-03 0.47E+00 0.46E-02 0.72E+00 0.18E-01 0.14E+01 0.17E+00
3.5 - 4.0 0.17E+00 0.33E-03 0.29E+00 0.17E-02 0.45E+00 0.68E-02 0.90E+00 0.65E-01
4.0 - 4.5 0.11E+00 0.14E-03 0.19E+00 0.75E-03 0.30E+00 0.30E-02 0.62E+00 0.29E-01
4.5 - 5.0 0.74E-01 - 0.13E+00 0.35E-03 0.21E+00 0.14E-02 0.44E+00 0.14E-01
5.0 - 6.0 0.90E-01 - 0.16E+00 0.28E-03 0.26E+00 0.11E-02 0.56E+00 0.11E-01
6.0 - 7.0 0.49E-01 - 0.92E-01 - 0.15E+00 0.37E-03 0.33E+00 0.37E-02
7.0 - 8.0 0.29E-01 - 0.55E-01 - 0.91E-01 0.14E-03 0.21E+00 0.14E-02
8.0 - 9.0 0.18E-01 - 0.35E-01 - 0.59E-01 - 0.14E+00 0.62E-03
9.0 - 10.0 0.12E-01 - 0.23E-01 - 0.40E-01 - 0.94E-01 0.29E-03
10.0 - 12.0 0.13E-01 - 0.23E-01 - 0.41E-01 - 0.10E+00 0.16E-03
12.0 - 14.0 0.67E-02 - 0.13E-01 - 0.23E-01 - 0.59E-01 -
14.0 - 16.0 0.37E-02 - 0.78E-02 - 0.14E-01 - 0.37E-01 -
16.0 - 18.0 0.23E-02 - 0.50E-02 - 0.93E-02 - 0.25E-01 -
18.0 - 20.0 0.14E-02 - 0.33E-02 - 0.63E-02 - 0.17E-01 -
TOTALS 32.53 54.14 24.66 38.84 19.55 29.16 14.79 20.22
– 25 –
Table 4. Multiplicity of Mg, Si, S and Fe Kα lines
∆E Mg Si S Fe
(MeV/nucleon) H-like He-like H-like He-like H-like He-like H-like He-like
0.5 - 1.0 0.21E-02 0.31E-01 - 0.38E-01 - 0.34E-02 - -
1.0 - 1.5 0.11E+00 0.12E+01 0.58E-02 0.62E+00 0.30E-03 0.11E+00 - -
1.5 - 2.0 0.66E+00 0.37E+01 0.73E-01 0.17E+01 0.69E-02 0.52E+00 - 0.22E-03
2.0 - 2.5 0.14E+01 0.39E+01 0.30E+00 0.23E+01 0.44E-01 0.11E+01 - 0.17E-02
2.5 - 3.0 0.17E+01 0.24E+01 0.64E+00 0.20E+01 0.14E+00 0.14E+01 - 0.72E-02
3.0 - 3.5 0.15E+01 0.11E+01 0.90E+00 0.14E+01 0.29E+00 0.14E+01 - 0.20E-01
3.5 - 4.0 0.12E+01 0.50E+00 0.97E+00 0.85E+00 0.45E+00 0.12E+01 0.22E-03 0.42E-01
4.0 - 4.5 0.86E+00 0.23E+00 0.89E+00 0.48E+00 0.56E+00 0.86E+00 0.68E-03 0.72E-01
4.5 - 5.0 0.64E+00 0.11E+00 0.76E+00 0.26E+00 0.60E+00 0.59E+00 0.17E-02 0.11E+00
5.0 - 6.0 0.85E+00 0.84E-01 0.11E+01 0.23E+00 0.11E+01 0.62E+00 0.11E-01 0.32E+00
6.0 - 7.0 0.51E+00 0.26E-01 0.72E+00 0.80E-01 0.85E+00 0.25E+00 0.30E-01 0.44E+00
7.0 - 8.0 0.32E+00 0.97E-02 0.47E+00 0.31E-01 0.61E+00 0.10E+00 0.65E-01 0.51E+00
8.0 - 9.0 0.22E+00 0.41E-02 0.32E+00 0.13E-01 0.44E+00 0.46E-01 0.11E+00 0.51E+00
9.0 - 10.0 0.15E+00 0.19E-02 0.23E+00 0.64E-02 0.31E+00 0.22E-01 0.16E+00 0.45E+00
10.0 - 12.0 0.19E+00 0.15E-02 0.29E+00 0.50E-02 0.40E+00 0.17E-01 0.42E+00 0.65E+00
12.0 - 14.0 0.11E+00 0.46E-03 0.17E+00 0.16E-02 0.23E+00 0.54E-02 0.45E+00 0.34E+00
14.0 - 16.0 0.66E-01 0.17E-03 0.10E+00 0.61E-03 0.15E+00 0.20E-02 0.39E+00 0.16E+00
16.0 - 18.0 0.43E-01 - 0.67E-01 0.26E-03 0.97E-01 0.88E-03 0.30E+00 0.76E-01
18.0 - 20.0 0.29E-01 - 0.46E-01 0.12E-03 0.67E-01 0.41E-03 0.23E+00 0.37E-01
20.0 - 25.0 0.42E-01 - 0.67E-01 0.10E-03 0.98E-01 0.36E-03 0.36E+00 0.32E-01
25.0 - 30.0 0.21E-01 - 0.33E-01 - 0.50E-01 - 0.19E+00 0.79E-02
30.0 - 35.0 0.12E-01 - 0.18E-01 - 0.28E-01 - 0.11E+00 0.25E-02
35.0 - 40.0 0.73E-02 - 0.11E-01 - 0.17E-01 - 0.71E-01 0.96E-03
40.0 - 45.0 0.48E-02 - 0.69E-02 - 0.11E-01 - 0.48E-01 0.42E-03
45.0 - 50.0 0.33E-02 - 0.46E-02 - 0.74E-02 - 0.33E-01 0.20E-03
50.0 - 55.0 0.23E-02 - 0.32E-02 - 0.52E-02 - 0.24E-01 0.11E-03
55.0 - 60.0 0.17E-02 - 0.23E-02 - 0.38E-02 - 0.18E-01 -
60.0 - 65.0 0.13E-02 - 0.17E-02 - 0.28E-02 - 0.14E-01 -
65.0 - 70.0 0.98E-03 - 0.13E-02 - 0.21E-02 - 0.11E-01 -
TOTALS 10.62 13.31 8.20 10.13 6.59 8.10 3.05 3.79
Table 5. Energies in keV of K X-ray lines from fast ions.
From Kelly (1987)
Projectiles H-like He-like
Kα line Kβ line Kα line Kβ line
C 0.37 0.44 0.31 0.35
N 0.50 0.59 0.43 0.50
O 0.65 0.77 0.57 0.67
Ne 1.02 1.21 0.92 1.07
Mg 1.47 1.74 1.35 1.58
Si 2.01 2.38 1.86 2.18
S 2.62 3.11 2.46 2.88
Fe 6.97 8.25 6.70 7.88
– 26 –
Table 6. Energies in keV of K
X-ray lines from ambient ions.
Elements EKα EKβ
C 0.29 -
N 0.40 -
O 0.53 -
Ne 0.85 -
Mg 1.25 -
Si 1.74 1.84
S 2.31 2.47
Ar 2.95 3.19
S 3.69 4.01
Fe 6.40 7.06
– 27 –
10-1 100 101 102
0123456789
10
(b)
CRS composition
E0=10 MeV/n
30 MeV/n
100 MeV/n
IB /
SEB
EX (keV)
10-1
100
101
10210
-1
100
101
102 Be
(a)
Ep=20 MeV
H
SEB
IB
SEB
IB
Be (Chu et al.)E
X d
σ/dE
X (
mb/
sr)
Fig. 1.— (a): Continuum X-ray production cross sections by a 20 MeV proton beam. The Chu
et al. (1981) data (solid curves) are for X-rays observed from a Be target at 90◦ to the beam; the
calculations, for both Be and H targets, are angle averaged; IB - inverse bremsstrahlung; SEB -
secondary electron bremsstrahlung. (b): Ratio of the inverse bremsstrahlung (IB) to the secondary
electron bremsstrahlung (SEB) productions, calculated from equation (1), for accelerated particle
with CRS composition and spectra given by equation (2) and interacting with an ambient medium
of solar composition.
– 28 –
1 1010
-22
10-21
10-20
10-19
10-18
10-17
10-16
10-15
10-14
Closed symbols: K X-ray productionOpen symbols: total electron capture
F9+
+Kr
F9++N
F9+
+Ar
F9++HO
8++He
Cro
ss s
ectio
n (c
m2 )
En (MeV/nucleon)
Fig. 2.— Charge exchange cross sections. The sources of the K X-ray production data are: F 9++H
– Hopkins, Little & Clue (1976a); O8++He – Guffey, Ellsworth & Macdonald (1977); F 9++Ar and
F 9++Kr – Hopkins et al. (1976b). The F 9++N total electron capture data is from Macdonald et
al. (1972). The theoretical curves employ the Nikolaev (1967) formalism with a single normalization
constant of 0.1 for the five different cross sections; solid curves – K X-ray production cross sections;
dashed curve – total electron capture cross section.
– 29 –
1 1010
-20
10-19
10-18
He
H
x2
F7+
F8+
F7+
F8+
Cro
ss s
ectio
n (c
m2 )
En (MeV/nucleon)
Fig. 3.— Excitation cross sections for fast F8+ and F7+ interacting in H and He. The data are from
Hopkins et al. (1976a). The curves were obtained by using the plane-wave-Born-approximation
(Bates 1962).
– 30 –
1 100.0
0.2
0.4
0.6
0.8
1.0
(b)
F2
F1
F0
Cha
rge
frac
tion
En (MeV/nucleon)
1 1010-20
10-19
10-18
10-17
10-16
(a)
3 2 1 0
4321C
ross
sec
tion
(cm
2 )
electron capture ionization
Fig. 4.— (a): Electron capture and ionization cross sections as a function of kinetic energy per
nucleon, of fast O interacting in an ambient medium of solar composition. Each curve is labeled
with the number of bound electrons of the incident O (i.e. before the collision). (b): Equilibrium
charge fractions as a function of kinetic energy of fast O in a neutral medium of solar composition.
– 31 –
Fig. 5.— Differential Kα X-ray line multiplicities for H-like and He-like fast C, N, O and Ne slowing
down in an ambient medium with solar abundances as functions of the projectile kinetic energy
per nucleon En. The same multiplicities are listed in Table 3 and the line centroids are given in
Table 5. The Kβ multiplicities are 25% of the corresponding Kα multiplicities.
– 32 –
Fig. 6.— Differential Kα X-ray line multiplicities for H-like and He-like fast Mg, Si, S and Fe
slowing down in an ambient medium with solar abundances as functions of the projectile kinetic
energy per nucleon En. The same multiplicities are listed in Table 4 and the line centroids are
given in Table 5. The Kβ multiplicities are 25% of the corresponding Kα multiplicities.
– 33 –
10-1
100
101
102
10-24
10-23
10-22
10-21
10-20
FeSi
Fe
Si
O
C
Kα
Kβ
K X
-ray
pro
duct
ion
cros
s se
ctio
n (c
m2 )
En (MeV/nucleon)
Fig. 7.— Cross sections for the production of K X-ray lines for fast protons interacting with ambient
neutral C, O, Si and Fe. We do not consider Kβ X-rays from Mg and lighter atoms because such
atoms in their ground state do not have 3p electrons.
– 34 –
Fig. 8.— X-ray flux for the CRS composition with two values of E0. The calculations are normalized
to a 3-7 MeV nuclear gamma-ray flux of 10−4 photons cm−2 s−1. Photoelectric absorption is taken
into account with a H column density of 3×1021 cm−2. IB - inverse bremsstrahlung; SEB - secondary
electron bremsstrahlung.
– 36 –
Fig. 10.— Solid curves – calculated X-ray fluxes from Orion from fast particle interactions for the
CRS composition; dashed curves – extragalactic X-ray background flux. Panel (a) – calculated X-
ray flux normalized to the total observed 3-7 MeV nuclear gamma-ray flux from Orion, 1.28×10−4
photons cm−2 s−1, assumed to be distributed over 200 deg2; panel (b) – calculated X-ray flux
normalized to the observed nuclear gamma-ray flux of 3.3×10−5 photons cm−2 s−1 from a hot spot
in Orion of assumed size 9 deg2 centered at lII=213.6◦, bII=-15.7◦. The extragalactic flux is directly
proportional to the assumed source size. Photoelectric absorption is taken into account with the
same column density (NH=3×1021 cm−2) for the X-rays produced in Orion and the extragalactic
background. The same column density is used for the sources of the two panels.
– 37 –
Fig. 11.— Same as Figure 10 but for the WC composition except that different values of E0 are
used in Figures 10 and 11.
– 38 –
0 10 20 30 40 50 60 70 80 90 100 110
1
10
Hot spot (9 deg2)
Extragalactic XRB
CRS
OBWC
(b)
ROSAT
C
ount
rat
e in
the
R45
ene
rgy
band
E0 (MeV/nucleon)
0 10 20 30 40 50 60 70 80 90 100 110
10
100
Extragalactic XRB
Total source (200 deg2)
OBCRS
WC (a)
ROSAT
Fig. 12.— Comparison of the ROSAT R45 data for Orion with the calculated X-ray emission that is
expected to accompany the observed nuclear gamma-ray emission, as a function of the characteristic
energy E0 [Eq. (2)] for the CRS, OB and WC compositions. The R45 energy band extends from
0.47 to 1.2 keV. The calculated X-ray spectra and the extragalactic X-ray background spectrum
are convoluted with the ROSAT/PSPC response function to yield the R45 count rates. Panels (a)
and (b) correspond to the same source parameters and column density as panels (a) and (b) in
Figures 10 and 11.
– 39 –
10-1
100
101
102
100
101
102
(b)
γ-ray line
production
X-ray lineproduction
(dE
/dx)
ioni
zed /
(dE
/dx)
neut
ral
En (MeV/nucleon)
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.164
5
6
7
8 Zi=8
(a)Zi(eff)=Zi[1-exp(-220βi/Zi
2/3)]
Zi(eff)=Z
i[1-exp(-137β
i/Z
i
2/3)]
Ionized ambient medium
Neutral ambient medium
Eff
ectiv
e ch
arge
βi
Fig. 13.— Effective charge and energy loss of fast O in an ionized ambient medium of solar
composition compared with those in a neutral medium. Panel (a): dashed curve – calculated
effective charge as a function of projectile velocity assuming that the ambient H and He are fully
ionized and the heavier ambient elements are neutral; solid curves – adopted fits. The effective
charge formula for fast ions in a neutral medium is from Pierce and Blann (1968). Panel (b): ratio
of O energy loss in an ionized medium to the O energy loss in a neutral medium, as a function of
kinetic energy/nucleon. The effective charges are calculated as in panel (a). The temperature of
the ionized medium is 104 K. Also shown are the effective energy ranges of X-ray line and 3-7 MeV
gamma-ray line productions from fast O in the ionized medium.
– 40 –
10-1
100
101
102
103
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
Steady state, dW/dt=1038
erg/s
Time dependent, W=3.2 1050
erg
OxygenE0=30 MeV/nucl
<nH>=10 cm-3
100 ky
30 ky
10 ky
1 ky
0.1 ky
Y(E
) [n
ucle
i/(M
eV/n
ucle
on)]
E (MeV/nucleon)
Fig. 14.— Comparison of the instantaneous, differential accelerated O numbers in the steady state
and the time-dependent models. Dashed curve – differential equilibrium accelerated O number in
the steady state model, normalized to a deposited power dW/dt = 16∫∞
0 E dNdt (E)dE of 1038 erg/s.
This is the approximate power required to account for the observed nuclear gamma-ray lines,
independent of the average ambient density < nH >. Solid curves – Time-dependent differential
accelerated O number at different times ranging from 0.1·103 to 100·103 years after the initial
instantaneous injection, normalized to a total deposited energy W = 16∫∞
0 EQ(E)dE of 3.2·1050
erg. In 105 years the deposited energy for the steady state model will equal the total deposited
energy for the time-dependent model.